Similar definitions for operators \(B_1\)  and \(B_2\) . The problem in [1]} is that it assumes the law of marginal probability holds true, for instance, \(p(a_2b_2)=\sum _{a_1,b_1=\lbrace 0,1\rbrace }p(a_1a_2b_1b_2)\) . [1]} does not provide details on how the joint probability is defined. As discussed earlier, the joint probability cannot be well defined unless the measurement operators are commutative. If
assuming the classical probability axiom , i.e., \(p(a_1a_2b_1b_2)=p(a_2b_2|a_1b_1)p(a_1b_1)\) , the law of marginal probability is equivalent to the law of total probability such that
\(p(a_2b_2) = \sum _{a_1,b_1=\lbrace 0,1\rbrace }p(a_2b_2|a_1b_1,\rho )p(a_1b_1).\) 
